On Algebraically Integrable Differential Operators on an Elliptic Curve
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special elliptic curves defined over Q which do not deform to gener...
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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147170 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Algebraically Integrable Differential Operators on an Elliptic Curve / P. Etingof, E. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147170 |
|---|---|
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dspace |
| spelling |
irk-123456789-1471702019-02-14T01:25:43Z On Algebraically Integrable Differential Operators on an Elliptic Curve Etingof, P. Rains, E. We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special elliptic curves defined over Q which do not deform to generic elliptic curves. We also study algebraically integrable operators of higher order with several poles and with symmetries, and (conjecturally) relate them to crystallographic elliptic Calogero-Moser systems (which is a generalization of the results of Airault, McKean, and Moser). 2011 Article On Algebraically Integrable Differential Operators on an Elliptic Curve / P. Etingof, E. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35J35; 70H06 DOI:10.3842/SIGMA.2011.062 http://dspace.nbuv.gov.ua/handle/123456789/147170 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special elliptic curves defined over Q which do not deform to generic elliptic curves. We also study algebraically integrable operators of higher order with several poles and with symmetries, and (conjecturally) relate them to crystallographic elliptic Calogero-Moser systems (which is a generalization of the results of Airault, McKean, and Moser). |
| format |
Article |
| author |
Etingof, P. Rains, E. |
| spellingShingle |
Etingof, P. Rains, E. On Algebraically Integrable Differential Operators on an Elliptic Curve Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Etingof, P. Rains, E. |
| author_sort |
Etingof, P. |
| title |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_short |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_full |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_fullStr |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_full_unstemmed |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_sort |
on algebraically integrable differential operators on an elliptic curve |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147170 |
| citation_txt |
On Algebraically Integrable Differential Operators on an Elliptic Curve / P. Etingof, E. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT etingofp onalgebraicallyintegrabledifferentialoperatorsonanellipticcurve AT rainse onalgebraicallyintegrabledifferentialoperatorsonanellipticcurve |
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2023-05-20T17:26:46Z |
| last_indexed |
2023-05-20T17:26:46Z |
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1796153312247021568 |